This was my first thought as well. I've gotten decent at using photoshop to do this with generous use of cutouts and indexed color modes to custom forced palet

This was my first thought as well. I've gotten decent at using photoshop to do this with generous use of cutouts and indexed color modes to custom forced palettes, but it's a very laborious process. Playing with this, it's very effective for solid-color graphics as it quickly settles in on a nice limited palette. The line-work also does a reasonable job, limiting the manual fixing to areas where lines converge and so forth. I'm working on writing up a post for /r/crossstitch comparing some different methods, so check over there in a while if you're interested.